def Pxxx(xEdge, yEdge, zEdge):
# no | node | e1 | e2 | e3
# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
posX = [0, 0] if xEdge == 'eX0' else [
1, 0
] if xEdge == 'eX1' else [0, 1] if xEdge == 'eX2' else [1, 1]
posY = [0, 0] if yEdge == 'eY0' else [
1, 0
] if yEdge == 'eY1' else [0, 1] if yEdge == 'eY2' else [1, 1]
posZ = [0, 0] if zEdge == 'eZ0' else [
1, 0
] if zEdge == 'eZ1' else [0, 1] if zEdge == 'eZ2' else [1, 1]
ind1 = sub2ind(M.vnEx, np.c_[ii, jj + posX[0], kk + posX[1]])
ind2 = sub2ind(M.vnEy, np.c_[ii + posY[0], jj,
kk + posY[1]]) + M.nEx
ind3 = sub2ind(M.vnEz, np.c_[ii + posZ[0], jj + posZ[1],
kk]) + M.nEx + M.nEy
IND = np.r_[ind1, ind2, ind3].flatten()
PXXX = sp.coo_matrix((np.ones(3 * M.nC), (range(3 * M.nC), IND)),
shape=(3 * M.nC, M.nE)).tocsr()
if M._meshType == 'Curv':
I3x3 = inv3X3BlockDiagonal(
getSubArray(eT1[0], [i, j + posX[0], k + posX[1]]),
getSubArray(eT1[1], [i, j + posX[0], k + posX[1]]),
getSubArray(eT1[2], [i, j + posX[0], k + posX[1]]),
getSubArray(eT2[0], [i + posY[0], j, k + posY[1]]),
getSubArray(eT2[1], [i + posY[0], j, k + posY[1]]),
getSubArray(eT2[2], [i + posY[0], j, k + posY[1]]),
getSubArray(eT3[0], [i + posZ[0], j + posZ[1], k]),
getSubArray(eT3[1], [i + posZ[0], j + posZ[1], k]),
getSubArray(eT3[2], [i + posZ[0], j + posZ[1], k]))
PXXX = I3x3 * PXXX
return PXXX
def Pxxx(xFace, yFace, zFace):
"""
xFace is 'fXp' or 'fXm'
yFace is 'fYp' or 'fYm'
zFace is 'fZp' or 'fZm'
"""
# no | node | f1 | f2 | f3
# 000 | i ,j ,k | i , j, k | i, j , k | i, j, k
# 100 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k
# 010 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k
# 110 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k
# 001 | i ,j ,k+1 | i , j, k | i, j , k | i, j, k+1
# 101 | i+1,j ,k+1 | i+1, j, k | i, j , k | i, j, k+1
# 011 | i ,j+1,k+1 | i , j, k | i, j+1, k | i, j, k+1
# 111 | i+1,j+1,k+1 | i+1, j, k | i, j+1, k | i, j, k+1
posX = 0 if xFace == 'fXm' else 1
posY = 0 if yFace == 'fYm' else 1
posZ = 0 if zFace == 'fZm' else 1
ind1 = sub2ind(M.vnFx, np.c_[ii + posX, jj, kk])
ind2 = sub2ind(M.vnFy, np.c_[ii, jj + posY, kk]) + M.nFx
ind3 = sub2ind(M.vnFz, np.c_[ii, jj, kk + posZ]) + M.nFx + M.nFy
IND = np.r_[ind1, ind2, ind3].flatten()
PXXX = sp.coo_matrix((np.ones(3 * M.nC), (range(3 * M.nC), IND)),
shape=(3 * M.nC, M.nF)).tocsr()
if M._meshType == 'Curv':
I3x3 = inv3X3BlockDiagonal(
getSubArray(fN1[0], [i + posX, j, k]),
getSubArray(fN1[1], [i + posX, j, k]),
getSubArray(fN1[2], [i + posX, j, k]),
getSubArray(fN2[0], [i, j + posY, k]),
getSubArray(fN2[1], [i, j + posY, k]),
getSubArray(fN2[2], [i, j + posY, k]),
getSubArray(fN3[0], [i, j, k + posZ]),
getSubArray(fN3[1], [i, j, k + posZ]),
getSubArray(fN3[2], [i, j, k + posZ]))
PXXX = I3x3 * PXXX
return PXXX
def test_invXXXBlockDiagonal(self):
a = [np.random.rand(5, 1) for i in range(4)]
B = inv2X2BlockDiagonal(*a)
A = sp.vstack((sp.hstack((sdiag(a[0]), sdiag(a[1]))),
sp.hstack((sdiag(a[2]), sdiag(a[3])))))
Z2 = B*A - sp.identity(10)
self.assertTrue(np.linalg.norm(Z2.todense().ravel(), 2) < TOL)
a = [np.random.rand(5, 1) for i in range(9)]
B = inv3X3BlockDiagonal(*a)
A = sp.vstack((sp.hstack((sdiag(a[0]), sdiag(a[1]), sdiag(a[2]))),
sp.hstack((sdiag(a[3]), sdiag(a[4]), sdiag(a[5]))),
sp.hstack((sdiag(a[6]), sdiag(a[7]), sdiag(a[8])))))
Z3 = B*A - sp.identity(15)
self.assertTrue(np.linalg.norm(Z3.todense().ravel(), 2) < TOL)
def test_invXXXBlockDiagonal(self):
a = [np.random.rand(5, 1) for i in range(4)]
B = inv2X2BlockDiagonal(*a)
A = sp.vstack((sp.hstack((sdiag(a[0]), sdiag(a[1]))),
sp.hstack((sdiag(a[2]), sdiag(a[3])))))
Z2 = B*A - sp.identity(10)
self.assertTrue(np.linalg.norm(Z2.todense().ravel(), 2) < TOL)
a = [np.random.rand(5, 1) for i in range(9)]
B = inv3X3BlockDiagonal(*a)
A = sp.vstack((sp.hstack((sdiag(a[0]), sdiag(a[1]), sdiag(a[2]))),
sp.hstack((sdiag(a[3]), sdiag(a[4]), sdiag(a[5]))),
sp.hstack((sdiag(a[6]), sdiag(a[7]), sdiag(a[8])))))
Z3 = B*A - sp.identity(15)
self.assertTrue(np.linalg.norm(Z3.todense().ravel(), 2) < TOL)